On the local meromorphic extension of CR meromorphic mappings
Abstract
Let
M
be a generic CR submanifold in $\C^{m+n}$,
m=CRdimM≥1
,
n=codimM≥1
,
d=dimM=2m+n
. A CR meromorphic mapping (in the sense of Harvey-Lawson) is a triple
(f,
D
f
,[
Γ
f
])
, where: 1.
f:
D
f
→Y
is a
C
1
-smooth mapping defined over a dense open subset
D
f
of
M
with values in a projective manifold
Y
; 2. The closure
Γ
f
of its graph in $\C^{m+n} \times Y$ defines a oriented scarred
C
1
-smooth CR manifold of CR dimension
m
(i.e. CR outside a closed thin set) and 3. Such that
d[
Γ
f
]=0
in the sense of currents. We prove in this paper that
(f,
D
f
,[
Γ
f
])
extends meromorphically to a wedge attached to
M
if
M
is everywhere minimal and
C
ω
(real analytic) or if
M
is a
C
2,α
globally minimal hypersurface.